Zero-sum constrained stochastic games with independent state processes

We consider a zero-sum stochastic game with side constraints for both players with a special structure. There are two independent controlled Markov chains, one for each player. The transition probabilities of the chain associated with a player as well as the related side constraints depend only on the actions of the corresponding player; the side constraints also depend on the player’s controlled chain. The global cost that player 1 wishes to minimize and that player 2 wishes to maximize, depend however on the actions and Markov chains of both players. We obtain a linear programming formulations that allows to compute the value and saddle point policies for this problem. We illustrate the theoretical results through a zero-sum stochastic game in wireless networks in which each player has power constraints     

A new synthesis of α-amino acids—III: Amidoalkylation of active methylene compounds with glyoxylic acid derivatives

The synthesis of N-acyl derivatives of γ - keto - α - amino acids (3, 4, 5) by the amidoalkylation of 1,3-dicarbonyl compounds with glyoxylic acid-amide adducts (1, 2) is described. The γ - keto - α - amino acid derivatives (4, 5) were further converted to the corresponding butenolides (6, 7) and to pyrazolylglycine (12).     

Eigenmode scattering relations for plane-stratified gyrotropic media

We consider the 4×4 scattering matrixS for a plane wave incident on a plane-stratified gyrotropic multilayer slab, which is assumed to have a single symmetry axis (the magnetisation vector in a ferrite sheet, or the external magnetic field direction in a plane-stratified magnetoplasma). In the given (original) problem the plane of incidence is at an azimuthal angle ϕ with respect to the magnetic meridian plane (the plane containing the normal to the stratification, and the gyrotropic symmetry axis), and there is a corresponding “conjugate” set of wave fields, in which the plane of incidence is at an azimuthal angle (π−ϕ), with a corresponding conjugate scattering matrixS′. Adjoint wave fields, obtained by reversing the magnetic symmetry vector, are used to yield the eigenmode amplitudes required in the definition of the scattering matrices. At an interface between two adjacent layers the scattering matrices are shown to be uniquely determined by the characteristic wave polarisations, and this is used to prove that the given and conjugate scattering matrices,S andS′, for the overall multilayer system are mutually transposed, i.e. .     

Synthesis of 2-D-L-tryptophan by sequential Ir-catalyzed reactions

Herein, we report a practical synthesis of 2-D-l-tryptophan via sequential Ir-catalyzed CH borylation, and Ir-catalyzed C-2-deborylative deuteration steps. In this synthetic sequence, deprotection of the Boc and methyl ester groups proved challenging, due to replacement of deuterium with hydrogen. However, mild deprotection conditions were developed to avoid this D/H scrambling. Further, 2-D-L-Tryptophan is stable in many buffers used for biological studies.     

Substrate Envelope-Designed Potent HIV-1 Protease Inhibitors to Avoid Drug Resistance

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Copper‐Mediated Deoxygenative Trifluoromethylation of Benzylic Xanthates: Generation of a C?CF3 Bond from an O‐Based Electrophile

The conversion of an alcohol‐based functional group, into a trifluoromethyl analogue is a desirable transformation. However, few methods are capable of converting O‐based electrophiles into trifluoromethanes. The copper‐mediated trifluoromethylation of benzylic xanthates using Umemoto’s reagent as the source of CF₃ to form C? CF₃ bonds is described. The method is compatible with an array of benzylic xanthates bearing useful functional groups. A preliminary mechanistic investigation suggests that the C? CF₃ bond forms by reaction of the substrate with in situ generated CuCF₃ and CuOTf. Further evidence suggests that the reaction could proceed via a radical cation intermediate.     

SO(4) theory of antiferromagnetism and superconductivity in Bechgaard salts

Motivated by recent experiments with Bechgaard salts, we investigate the competition between antiferromagnetism and triplet superconductivity in quasi-one-dimensional electron systems. We unify the two orders in an SO(4) symmetric framework, demonstrating the existence of such symmetry in one-dimensional Luttinger liquids. SO(4) symmetry strongly constrains the phase diagram, leading to coexistence regions of antiferromagnetic, superconducting, and normal phases, as observed in (TMTSF)(2)PF(6). We predict a sharp neutron scattering resonance in superconducting samples.